If `L = (20 pm 0.01) m and B = (10 pm 0.02)m` then L/B is

Options

A. `(2 pm 0.03) m`
B. `(2 pm 0.015)m`
C. `(2 pm 0.01)m`
D. `(2 pm 0.005)m`

Answer

To solve the problem of finding \( \frac{L}{B} \) where \( L = (20 \pm 0.01) \, \text{m} \) and \( B = (10 \pm 0.02) \, \text{m} \), we will follow these steps:

### Step 1: Calculate the central value of \( \frac{L}{B} \)

We start by calculating the central value of \( \frac{L}{B} \):

\[ \frac{L}{B} = \frac{20 \, \text{m}}{10 \, \text{m}} = 2 \]

### Step 2: Determine the absolute uncertainties

Next, we need to find the absolute uncertainties in the values of \( L \) and \( B \). The uncertainties are given as:

- \( \Delta L = 0.01 \, \text{m} \)
- \( \Delta B = 0.02 \, \text{m} \)

### Step 3: Calculate the relative uncertainties

Now, we calculate the relative uncertainties for \( L \) and \( B \):

\[ \text{Relative uncertainty in } L = \frac{\Delta L}{L} = \frac{0.01}{20} = 0.0005 \]

\[ \text{Relative uncertainty in } B = \frac{\Delta B}{B} = \frac{0.02}{10} = 0.002 \]

### Step 4: Add the relative uncertainties

Since we are dividing \( L \) by \( B \), we add the relative uncertainties to find the total relative uncertainty in \( \frac{L}{B} \):

\[ \text{Total relative uncertainty} = \text{Relative uncertainty in } L + \text{Relative uncertainty in } B = 0.0005 + 0.002 = 0.0025 \]

### Step 5: Calculate the absolute uncertainty in \( \frac{L}{B} \)

To find the absolute uncertainty in \( \frac{L}{B} \), we multiply the total relative uncertainty by the central value of \( \frac{L}{B} \):

\[ \Delta \left(\frac{L}{B}\right) = \text{Total relative uncertainty} \times \frac{L}{B} = 0.0025 \times 2 = 0.005 \]

### Step 6: Write the final result

Now we can write the final result for \( \frac{L}{B} \) with its uncertainty:

\[ \frac{L}{B} = 2 \pm 0.005 \]

### Final Answer

Thus, the final answer is:

\[ \frac{L}{B} = 2 \pm 0.005 \, \text{m} \]

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